Le système SI et son évolution; le rôle de la seconde dans le future SI Terry Quinn

Transcription

1 Le système SI et son évolution; le rôle de la seconde dans le future SI Terry Quinn Directeur honoraire du Bureau International des Poids et Mesures (BIPM)

2 TJQ and Jean Kovalevsky at the French Archives on 16 November 2010 with the Metre and Kilogram of the Archives deposited there on 22 June 1799 Photo TJQ

3 La Convention du Mètre 1875 The safe in the vault of the prototypes at the BIPM where the kilogram and metre rested from 1889 until 1998 when they were transferred to a new safe.

4 A K mol s cd m kg The base units of the SI situation today

5 The SI In November 2018 the SI embraces quantum physics. From artefacts to atoms at last!

6 26 ieme CGPM novembre 2018: le Système international d'unités, le SI, sera le système d unités selon lequel : la fréquence de la transition hyperfine dans l état fondamental de l atome de césium 133 ΔνCs est hertz, la vitesse de la lumière dans le vide c est mètres par seconde, la constante de Planck h est xx joule seconde, la charge élémentaire e est xx coulomb, la constante de Boltzmann k est égale à xx joule par kelvin, la constante d'avogadro N A est xx par mole, l'efficacité lumineuse K cd d'un rayonnement monochromatique de fréquence Hz est 683 lumens par watt,

7 Table 1. The seven defining constants of the SI, and the seven corresponding units they define Defining constant Symbol Numerical value Unit hy hypererfine transition frequency of Cs Δ ν Cs Hz (s -1 ) speed of light in vacuum c m s 1 Planck constant h xx kg m 2 s -1 elementary charge e xx C (As) Boltzmann constant k xx kg m 2 s -2 K -1 Avogadro constant N A xx 1023 mol 1 luminous efficacy K cd 683 cd sr kg -1 m -2 s 3 (lm W 1 ) This shows the hierarchical nature of the new definitions. We begin with the second, then knowing the second we can define the metre, then knowing the second and the metre we can define the kilogram and so on The mole is the only one that does not include any of the other units.

8 What does it mean to define the numerical value of a fundamental constant of physics surely these are fixed by nature? The value of a constant of physics is indeed fixed by nature but its numerical value depends on the size of the unit with which we choose to measure it, take for example the speed of light:

9 the speed of light, c may be written: c = metres per second or c = feet per second or c = yards per second the value of c = numerical value unit The value of c is a constant of nature. 1. If we define the units independently, then we must determine the numerical value of c by experiment, and it will have an uncertainty. That was the situation before 1983, when both the metre and the second were independently defined. 2. If the second is independently defined in terms of the frequency of the caesium transition, and we choose to fix the numerical value of c, then the effect is to define the size of the unit, equal to in the case of the metre. This is the current definition of the metre, since the change in The numerical value now has zero uncertainty. 3. We have thus defined the metre in terms of a fixed numerical value for the speed of light.

10 How do we make practical use of such a definition? We need to find an equation of physics that links the speed of light to length without including any unknown constants or quantities that themselves depend on length, such an equation is c = λ f Where λ is the wavelength of a light of frequency f. We could also of course simply measure the time taken for a light signal to travel from one place to another but this is not practical for short distances.

11 Let us now look at the Planck constant, h h = xx kg m 2 s 1 value of h = numerical value unit The value of h is a constant of nature. 1. If we define the unit kg m 2 s -1 independently, then we must determine the numerical value of h by experiment, and it will have an uncertainty. That is the present situation, this is what we are doing at present with watt (Kibble) balances and silicon spheres. 2. However, if the metre and the second are already independently defined, we can choose to fix the numerical value of h, then the effect is to define the size of the kilogram. This is the proposed new definition of the kilogram. The numerical value will have zero uncertainty. We just have to make sure we choose the right value i.e., one that is really consistent with the present definition of the kilogram. This is why we do it in two independent ways.

12 The key question is however the following: How can we be sure that the numerical value we choose for these defining constants are the right ones, i.e., that when the new definitions are implemented there will not be a step change in the size of the units? We do the measurements of the Planck constant by two methods: The first is by means of a watt balance, which we now call the Kibble balance in which electrical power is compared with mechanical power to give a value for h

13 The Kibble balance But we cannot directly measure either L or B with sufficient accuracy

14 Combining the equations from the two configurations gives mgv = IU Taking advantage of the Josephson effect, which gives a voltage U = nfh/2e and the quantum- Hall effect, which gives an electrical resistance R = h/ie 2 we can write IU = in 2 f 2 h/4 so that mgv = in 2 f 2 h/4 which gives: h = 4mgv/in 2 f 2

15 NIST watt balance Mk II

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17 Lego Kibble balance; accuracy about 5%

18 silicon spheres weighing about 1 kg containing about atoms Photo BIPM

19 For the silicon crystal density we have: N A = n M(Si)/ρ a 3 Where n is the number of atoms per unit cell of silicon, M(Si) the molar mass of silicon, ρ the density of the sample of silicon and a its lattice constant so that, remembering that N A h = [cα 2 /2R ][M u A r (e)], where α, R, M u and A r (e) are the fine structure constant (known to parts in ), the Rydberg for infinite mass (parts in ), the molar mass constant (exact) and the relative atomic mass of the electron (parts in ) respectively. h (silicon) = [cα 2 /2R ][M u A r (e)] ρ a 3 / n M(Si)

20 From the Kibble balance we have: h = 4mgv/in 2 f 2 From the silicon sphere we have: h (silicon) = [cα 2 /2R ][M u A r (e)] ρ a 3 / n M(Si) The two give the same value for h to within a few parts in 10 8 which is absolutely remarkable!

21 New BIPM set of reference mass standards. In the future their mass will be determined by the Kibble balance and silicon density determinations

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